In the most elementary \(K=2\)  CHSP scenario
it is not easy to keep the physics given by
the respective candidates \(\mathfrak {h}\)  and \(\Omega \,\) 
for the Hamiltonian and mapping
fully under control.
One must be even more careful when
using the inverted flowchart \(H \rightarrow \Theta \rightarrow \Omega \) 
as discussed by Scholtz et al [1]}.
In an ideal situation,
the determination of an optimal \(\Omega \) 
should not be based on the mere
educated guess.
One may expect an improvement of the results, in particular, after
the above-described multi-step
relegation of the
Hermiticity of
operators from \({\cal R}_{j}\)  to \({\cal R}_{j+1}\) .
